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The volume of a cube is numerically equal to four times the sum of the lengths of its edges. What is the volume, in cubic units, of the cube? Express your answer in simplest radical

 Jul 18, 2022
 #1
avatar+27 
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12sqrt(3) 12*edge*4=x^3 the area so the edge or x=4sqrt(3) 4sqrt(3)^3=area so it is 12sqrt(3)

 Jul 18, 2022
edited by MathBreathing  Jul 18, 2022
edited by MathBreathing  Jul 18, 2022
 #4
avatar+99 
+1

Um i think this is wrong

pogfrog123456789  Jul 18, 2022
edited by pogfrog123456789  Jul 18, 2022
 #2
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the lentgh of all edges is 12 and sqrt(12) is 2sqrt(3)
SO THE ANSWER IS 2sqrt(3)

 Jul 18, 2022
 #6
avatar+2448 
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Let the side of the cube be \(s\). We have the equation \(s^3 = 4 \times 12s\)

 

Solving the equation gives us \(s = \sqrt{48} = 4 \sqrt{3}\)

 

So, the volume of this is \((4 \sqrt 3)^3 = \color{brown}\boxed{192 \sqrt 3}\)

 Jul 18, 2022
 #7
avatar+99 
0

uh thanks

pogfrog123456789  Jul 18, 2022

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